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I think it's actually higher (though I don't have a quick way of thinking how much higher. Maybe I'll think about it some more). Because 162 Tigers wins mean that everyone else loses at least their games to the Tigers, which means that 162 Tiger wins is < Tigers' wins + opponents' losses.

Think of it this way: in a one game playoff, the magic number is 2: a combo of one victory for us plus one defeat for them.

In a three game playoff, the magic number is four (two victories for us, two defeats for them).

But if it isn't pairwise, it's harder to figure out. In a round robin (hmm....) with three teams, my team would definitely win if we won two which would mean our magic number is four: two wins for us plus two losses for the others. Okay, with a five team pool, if we won four, they'd lose at least four. So is our magic number 10? (*thinks*)

Us: 3-1Yankees: 3-1Red Sox: 2-2White Sox: 1-3Angels: 1-3

So that doesn't work. Maybe you have to think of the magic number pairwise. So my magic number with respect to any single other team is 162 (I go 82-80, they go 80-82). But to be guaranteed victory I think you'd have to worry about going let's say 154-8, against a team that won all its games except the 8 it played with you, while you lost 8 to a team they beat. Now of course you're all playing outside your division and also (alas!) outside your league, so the intradivision losses don't have to match up with the intradivision wins.

apologies for the belated reply. work, as you say, and life, which i read elsewhere has much of moment for you as well.

i like your analysis, and i agree that the magic number is designed for pairwise consideration.

however, i should say (should've said in the entry perhaps), that i was looking at it poetically: riffing on the term of art and referring to a number that's magical for another reason: 162 represents the blank slate, the start of the new season, the opportunity to go out and make history, and the number of opportunities to watch one's team in action (playoffs or not, everyone's guaranteed 162).

back to the term of art: although i understand that the operation of reduction includes losses by the trailing team, i like to take the (pessimist's?) point of view that the trailing team is going to win the remainder of its games (it can happen at the tail end of the season -- has happened to the tigers' detriment) and treat the number solely as the number of games the team must win in order to seize the division. (that the number falls more rapidly than such a perception would allow is always a pleasant surprise.)

i should probably therefore also track a 'jones index number' that doesn't care about the other teams. call it 94. any team in our division that can win 94 games is probably going to win the division. so i would reduce the number with each win, ignoring others' losses. if at any point in the season the adjusted jones index is higher than the remaining number of games (say, a record of 50-69 with a resulting jones number of 44 and only 43 games remaining) the team would effectively be eliminated, to an almost near-certainty (call it a crash). only if a team makes it to september without crashing are they then assigned a magic number.

and you're right about the impact of teams playing against divisional opponents -- the wiki article demonstrates that it is quite possible for a trailing team's magic number to be inaccurate when multiple teams ahead of it will be playing against each other.